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THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN

Published online by Cambridge University Press:  02 September 2013

J. C. NAVARRO ,
J. D. ROSSI ,
A. SAN ANTOLIN  and
N. SAINTIER
J. C. NAVARRO
Affiliation:
Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 AlicanteSpain e-mails: jc.navarro@ua.es, julio.rossi@ua.es, angel.sanantolin@ua.es
J. D. ROSSI
Affiliation:
Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 AlicanteSpain e-mails: jc.navarro@ua.es, julio.rossi@ua.es, angel.sanantolin@ua.es
A. SAN ANTOLIN
Affiliation:
Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 AlicanteSpain e-mails: jc.navarro@ua.es, julio.rossi@ua.es, angel.sanantolin@ua.es
N. SAINTIER
Affiliation:
Departamento de Matemática, FCEyN Universidad de Buenos Aires (1428) Buenos Aires, Argentina, and Instituto de Ciencias – Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, C.P. 1613 Los Polvorines, Pcia de Bs. As., Argentina e-mails: nsaintie@dm.uba.ar; nsaintie@ungs.edu.ar
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Abstract

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In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples.

Keywords

35J6035P30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 241 - 249
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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